Wentzville School District
Unit 3: Product, Quotient, and Chain Rules for Derivatives
Stage 1 – Desired Results
Unit 3 – Product, Quotient and Chain Rules for Derivatives
Unit Title: Product, Quotient and Chain Rules for Derivatives
Course: Calculus
Brief Summary of Unit: In this unit students will extend their knowledge of derivatives by applying the power rule,
quotient rule and chain rule. In addition, students will find derivatives of trigonometric functions.
Textbook Correlation: Calculus 4th edition by Robert T. Smith, Roland B. Minton Chapter 2.4-2.6
*Derivatives of Trigonometric Functions will be covered in Unit 3 after Product, Quotient and Chain Rule.
Time Frame: 10-13 days
WSD Overarching Essential Question
Students will consider…














How do I use the language of math (i.e. symbols,
words) to make sense of/solve a problem?
How does the math I am learning in the classroom
relate to the real-world?
What does a good problem solver do?
What should I do if I get stuck solving a problem?
How do I effectively communicate about math
with others in verbal form? In written form?
How do I explain my thinking to others, in written
form? In verbal form?
How do I construct an effective (mathematical)
argument?
How reliable are predictions?
Why are patterns important to discover, use, and
generalize in math?
How do I create a mathematical model?
How do I decide which is the best mathematical
tool to use to solve a problem?
How do I effectively represent quantities and
relationships through mathematical notation?
How accurate do I need to be?
When is estimating the best solution to a
WSD Overarching Enduring Understandings
Students will understand that…










Mathematical skills and understandings are used
to solve real-world problems.
Problem solvers examine and critique arguments
of others to determine validity.
Mathematical models can be used to interpret and
predict the behavior of real world phenomena.
Recognizing the predictable patterns in
mathematics allows the creation of functional
relationships.
Varieties of mathematical tools are used to
analyze and solve problems and explore concepts.
Estimating the answer to a problem helps predict
and evaluate the reasonableness of a solution.
Clear and precise notation and mathematical
vocabulary enables effective communication and
comprehension.
Level of accuracy is determined based on the
context/situation.
Using prior knowledge of mathematical ideas can
help discover more efficient problem solving
strategies.
Concrete understandings in math lead to more
problem?
abstract understanding of math.
Transfer
Students will be able to independently use their learning to…
when and how to use rules/formulas and follow algorithms.
Meaning
Essential Questions
Understandings
Students will consider…
Students will understand that…
●
●
How do I recognize when to use which derivative
rule?
What is the best method for finding the derivative
of this function?
●
There are rules for taking the derivative of more
complex functions.
Acquisition
Key Knowledge
Key Skills
Students will know…
Students will be able to….
●
●
●
●
The product rule.
The quotient rule.
The chain rule.
Derivatives of the 6 trigonometric functions
●
●
●
●
●
●
●
●
Recognize when a function requires more than
just the basic differentiation rules.
Communicate when to use the product, quotient
and/or chain rule(s).
Find derivatives of more complex functions that
require the use of the product, quotient and chain
rule(s).
Find higher order derivatives.
Recognize multiple notations for derivatives.
Write equations of tangent lines at a given point.
Use technology to find derivatives and tangent
equations.
Find the derivative of functions that include
trigonometric expressions.
Standards Alignment
MISSOURI LEARNING STANDARDS
MP.1 Make sense of problems and persevere in solving them.
MP.2 Reason abstractly and quantitatively.
MP.3 Construct viable arguments and critique the reasoning of others.
MP.4 Model with mathematics.
MP.5 Use appropriate tools strategically.
MP.6 Attend to precision.
MP.7 Look for and make use of structure.
MP.8 Look for and express regularity in repeated reasoning.
SHOW-ME STANDARDS
Goal 1: 1, 4, 5, 6, 7, 8
Goal 2: 2, 3, 7
Goal 3: 1, 2, 3, 4, 5, 6, 7, 8
Goal 4: 1, 4, 5, 6
Mathematics: 1, 4, 5